String theory and 6D Yau-Calibi like protein folding?

In string theory, a solution involving flat 10D space seems like a valid solution. The Universe could be described by a solution that is 10D space, all large and flat. Of course for string theory to describe our universe, 3D remain large and flat, and 6D or 7D are curled up in a Yau Calibi manifold.

What I'm wondering is whether this folding of the other dimensions occurs "spontaneously" the way that proteins start out as a single 1D string of amino acids then due to thermodynamics and interactions with water and ions, spontaneously fold into a 3D structure (that is difficult to predict based solely on sequence of amino acids alone)

does the universe in string theory spontaneously fold itself in such a way that 3 remain large and extended, and 6 or 7 fold up, and does it fold up only in 1 way or can it fold up many ways.

Suppose it were possible to probe the planck energies with a particle accelerator, would string theory predict multiple possible conformations of these Yau-Calibi spaces? Do these spaces stay frozen and unchanging, even at planck energies? Does dark energy and inflationary expansion affect these hidden dimensions as they do large 3d dimensions?

Were these hidden dimensions affect the way the Big Bang happened and its inflation? Did they fold or refold them or were they already in that configuration prior to the Big Bang?

I'm a little bit confused as to whether it is 6D as in SUSY or 7D as in M-theory.

I understand that KKLT allows for a positive CC using a very complex system of branes wrapping around Yau Calibi manifolds followed by anti-branes. Is this sort of thing supposed to happen spontaneously? Do Yau Calibi manifolds with magnetic fluxes naturally fold up with branes and anti-branes?

First of all, I'm guessing that most of your question are too complicated to be answered by anyone, at least with certainty.

I don't think anyone can derive in detail from string theory how these 6 compact dimensions could emerge from a 10D spacetime, or how this would behave around the Big Bang in a string theory based cosmology.

The geometry of space-time is dynamic, also in string theory. The 4D large space-time + 6D Calabi-Yau is a simple vaccum solution which would become modified and spacetime dependent in a realistic universe. Just like ordinary general relativity.

Any matter content of the universe would influence also these dimensions in the same manner that they influence the 4 large dimensions.

An interesting matter is if string theory allows a process whereby this compact manifold changes its topology. I believe that on some level at least, this has been answered to the affirmative.

I don't think anyone knows much about the details of the big bang, even in string cosmology. And not how this would affect compact dimensions. But I may be wrong... :-)